Spectral Resolution of a Linear Operator

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Spectral Resolution of a Linear Operator

 

(or spectral representation of a linear operator), a representation of a linear operator A in the form of a linear combination of the projection operators to mutually perpendicular axes or, more generally, in the form of a special integral whose integrand is a family of projection operators satisfying certain conditions. This family of projection operators is known as the resolution of unity corresponding to A. The study of spectral resolutions and their possible generalizations for different types of linear operators makes up the principal content of the spectral analysis of linear operators.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.